What happens when two black holes meet?

Although I have a basic knowledge of blackholes and the effect they have on matter, I have a question as to what happens when two black holes meet?
Also, what would happen if two black holes of equal mass were equal distance from a stationary object in space, would the object be held in equlibrium by the two equal forces?

P.S. sorry if there are severe flaws with my theory but I have a rather limited knowledge of physics

Your second question involves a very unstable situation. Any tiny movement of the object in the middle would lead to it going in the direction of the closer black hole. Also, in your picture, what keeps the black holes from pulling together into one big one, swallowing up the object in the middle?

Ah, I see. I was assuming that the two blackholes were at equal distance to the object and were outside of each other's gravitational field. I thought that if the conditions were perfect the object could be held in perfect equilibrium.
Also, what is the general size of a blackhole's gravitational field and how close would it need to to have an effect on, for example, the movement of planets orbitting a star?

P.S. I understand that it is unlikely any two blackholes would be the same size and mass but this all just "theoretical"

Ah, I see. I was assuming that the two blackholes were at equal distance to the object

The thing is, the 3 objects would not be stationary with respect to each other (some kind of orbit involved)...plus, the gravity from other objects in the area would nudge/disrupt any precise equilibrium as mathman noted.

and were outside of each other's gravitational field....Also, what is the general size of a blackhole's gravitational field and how close would it need to to have an effect on, for example, the movement of planets orbitting a star?

As modeled by Einstein's General Relativity, gravity fields extend to infinity. So, the net effect is determined from the combined influences of many nearby objects. The strength of the gravity field declines quickly with distance (inverse square law) so the closest/most massive objects have the most influence (and the influence of extremely distant...or low mass...objects can often be negligible to the system).

P.S. I understand that it is unlikely any two blackholes would be the same size and mass but this all just "theoretical"

Be careful throwing around the word "theory"/"theoretical". In science, a "theory" has a specific meaning (it's an explanation that already has a good amount of supporting evidence...it's not a guess or a hunch as might be suggested by the everyday/non-scientific use of the word).